A principal twistor model is built whose slices uniquely recover the twistor spaces of algebraic hyperkähler metrics on Y that are asymptotic to a given cone metric on the regular locus of X, yielding an inclusion of the moduli space into a finite-dimensional real vector space.
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Principal twistor models and asymptotic hyperk\"ahler metrics
A principal twistor model is built whose slices uniquely recover the twistor spaces of algebraic hyperkähler metrics on Y that are asymptotic to a given cone metric on the regular locus of X, yielding an inclusion of the moduli space into a finite-dimensional real vector space.